Question

The mean weight of 60 students in a class is 40 kg. The mean weight of boys is 50 kg while that of girls is 30 kg. Find the number of boys and girls in the class.

Answer 1

Total number of students = 60
Mean weight of 60 students = 40
Let the number of boys = x
Then, the number of girls = 60 - x

Mean weight of boys = `" Total weight of boys"/"Total number of boys"`

⇒ 50 = `" Total weight of boys"/"x"`

⇒ Total weight of boys = 50x

Mean weight of girls = `" Total weight of girls"/"Total number of girls"`

⇒ 30 = `" Total weight of girls"/"60 - x"`

⇒ Total weight of girls = 30( 60 - x )

Now,
Mean weight of 60 students = `" Total weight of boys + Total weight of girls"/" Total number of students"`

⇒ 40 = `[ 50x + 30( 60 - x )]/60`

⇒ 2400 = 50x + 1800 - 30x
⇒ 20x = 600
⇒ x = 30
⇒ 60 - x = 60 - 30 = 30
Hence, the number of boys is 30 and the number of girls is also 30.